The wavelength independent interferometer disclosed in the parent of which the present application is a continuation in part discloses a polychromatic interferometer in which, in one embodiment, the output beams of two lasers are coaxially combined in the polychromatic interferometer to produce two independent and superimposed-in-registration interferograms of the one optical component under test. This interferometer admits the possibility of forming a long equivalent wavelength interferogram corresponding to a synthetic wavelength which is equal to the product of the two operational wavelengths divided by the difference. Since the spatial frequency of the fringe pattern associated with any particular source wavelength is inversely related to that wavelength, a simpler relationship between component and derived interferograms exists: The spatial frequency of the long equivalent wavelength interferogram is simply the difference in spatial frequencies associated with the two component wavelengths. Consequently, the apparent or effective frequency of the combined laser light is significantly lower than the actual frequency of the visible light of each such laser. The present invention relates to a process for extracting the information of such a two-wavelength interferogram to produce a long-equivalent wavelength interferogram. The interference or fringe pattern of the resulting interferogram would have been derived directly had a laser or other light source of a frequency equal to the difference between the two actually used laser frequencies been utilized instead. The above-derived long-equivalent wavelength interferogram is then suitable for conventional fringe processing whereby the surface topography or wavefront distortion associated with the component under test--for example, an aspheric surface such as the human cornea may be extracted.
The most straightforward method for extracting long equivalent wavelength information is by means of a multiplicative combination of the two fundamental interferograms. When, for example, two interferograms are combined multiplicatively, the product interferogram may be decomposed into four component interferograms: Two interferograms have fringe spatial frequencies corresponding to the inverse of each of the two component wavelengths and two additional interferograms having fringe spatial frequencies corresponding to sum and difference fringe spatial frequencies. This last difference spatial frequency corresponds to the long equivalent wavelength interferogram of interest.
As such, this product interferogram is amenable to spatial filtering techniques in the Fourier plane whereby, with the appropriate Fourier transform optics, spatial filtering and inverse transformation optics, a interferogram containing only the long equivalent wavelength information is produced. This in turn admits the use of a lower spatial resolution detector commensurate with the sensitivity reduction associated with the "coarser" long equivalent wavelength fringes.
There are at least two ways one may realize the product interferogram. One such way is by serial recording: Specifically, the first interferogram is recorded, developed and then "played back" with interferogram number two. This however, is not a particularly useful technique if the object being subjected to the interferogram measurement technique is not stationary as in the case for example of keratometers used for in-vivo measurements of the human cornea wherein the results will reflect a combination of surface topography as well as motion effects. An additional, possible multiplicative technique comprises parallel recording wherein the two different wavelength interferograms are formed on separate high spatial resolution detectors and then multiplied in the digital domain.
One possible alternative to multiplicative techniques is some form of extraction method that relies on the summing of the two interferograms. In fact, the invention disclosed in the aforementioned parent application is particularly appropriate for use in summing techniques for information extraction. The interferometer described therein is capable of producing a single interferogram which is the sum of the two interferograms that would otherwise be derived at the independent wavelengths of the two laser sources. Unfortunately, simply adding the two interferograms together does not produce the desired information. More specifically, when two interferograms are present simultaneously and are spatially superimposed, a single detector can record only the incoherent sum of the irradiances and thus the sum contains no more information than a DC component and components with spatial frequencies corresponding to the individual wavelengths operating in the interferogram. A simple sum does not produce any frequency components corresponding to the sum or difference of the frequencies of the independent sources and the lack of any different frequency components in that sum means that there is no long-equivalent wavelength interferometric information that can be extracted therefrom.
There is therefore a need for an extraction process for use with a long equivalent wavelength interferometer which avoids the aforementioned deficiencies of multiplicative processes and which exploits the summing characteristic of spatially superimposed interferograms such as may be readily provided by the wavelength independent interferometer disclosed in the aforementioned parent application.